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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 14.384 Time Series Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Breaks 1 14.384 Time Series Analysis, Fall 2007 Professor Anna Mikusheva Paul Schrimpf, scribe October 30, 2007 Lecture 15 Breaks and Cointegration Breaks Suppose y t = t x t- 1 + t , where t = ( t t , x t is stationary, and E [ t | I t ] = 0. We want to test + t > t H : = 0. There is a nuisance parameter, t , which is identified under the alternative, but not under the null hypothesis. If we knew t , we could just do an F-test. t F T ( SSR 1 ,T ) =- ( SSR 1 ,t + SSR t +1 ,T ) T 2 if t = [ T ] ( SSR 1 ,t + SSR t +1 ,T ) / ( T- k ) k where SSR t,s is the sum of squared residuals from OLS using the sample from time t to time s , and k is the number of restrictions (the dimension of ). This test is valid when t is known. When t is not known, we must use a different test. One test-statistic is the Quant statistic t Q = sup F T ( [ T ] t [(1- ) T ] ) (1) T Andrews (1993) derived the distribution of this statistic. Other test statistics are the mean Wold : 1 MW = T- T- 2 t X t F T ( = r ) , = [ T ] (2) T and the Andrews-Ploberger (1994) AP = ln " 1 T- T- 2 t X exp = r 1 t F T ( 2 ) T # (3) To derive the limiting distribution of these statistics, we must look at the behavior of SSR . Let be the OLS estimate from the sample from t = 1 , .., ....
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lec15 - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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